Robust evaluation of the dissimilarity between interrogation windows in image velocimetry

Image velocimetry techniques, which extract motion information by comparison of image regions, typically make use of cross-correlation to measure the degree of matching. In this work, a novel measure of the dissimilarity between interrogation windows is proposed which is based on a more robust estimator than cross-correlation. The method is validated on synthetic images and on two experimental data sets obtained from a periodically pulsed jet and a backward-facing step. The former is a basically laminar flow, whereas the latter is fully turbulent. Both of them are characterized by regions of high velocity gradients. The efficiency of the robust image velocimetry (RIV) is compared with a cross-correlation algorithm (PIV). The analysis of results shows that the RIV is less sensitive to the appearance and disappearance of particles, and to high velocity gradients and, in general, to noise, generating less spurious velocity vectors. As a consequence RIV resolves better the vorticity peaks at the center of the vortex rings generated by the pulsed jet, obtaining, for a given interrogation window size, a higher spatial resolution. Moreover, in the analysis of the flow field generated by the backward-facing step, the RIV performs better in the shear layer at the border of the recirculation region, leading to a more reliable estimation of Reynolds shear stress and horizontal velocity component.     

Effect of resolution on the speed and accuracy of particle image velocimetry interrogation

Particle image velocimetry incorporates a process by which an image of a flow field, bearing double images of seeding particles, is analyzed in small regions called “interrogation spots.” Each spot is imaged onto a photodetector array whose digitized output is evaluated computationally using the auto-correlation technique. This paper examines the effects of resolving the spot using arrays of various resolutions, motivated primarily by a gain in speed. For this purpose, two specially created test photographs representing (i) uniform flow and (ii) solid body rotation, were interrogated using array sizes ranging from 32 × 32 to 256 × 256. Each reduction in resolution by a factor of two gains a factor of four in interrogation speed, but this benefit is counteracted by a loss in accuracy. The particle image diameter strongly influences accuracy through two distinct error mechanisms. When the particle image is small compared to the pixel size, mean bias error becomes significant due to finite numerical resolution of the correlation function. Conversely, when the particle image is large, random error due to irregularities in the electronic images predominates. The optimum image size, therefore, lies not at either extreme but at an intermediate value such that the particle image is small in an absolute sense, and yet large relative to the pixel size. A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 September 1990     

Stereoscopic particle image velocimetry

Stereoscopic particle image velocimetry (PIV) employs two cameras to record simultaneous but distinct off-axis views of the same region of interest (illuminated plane within a flow seeded with tracer particles). Sufficient information is contained in the two views to extract the out-of-plane motion of particles, and also to eliminate perspective error which can contaminate the in-plane measurement. This review discusses the principle of stereoscopic PIV, the different stereoscopic configurations that have been used, the relative error in the out-of-plane to the in-plane measurement, and the relative merits of calibration-based methods for reconstructing the three-dimensional displacement vector in comparison to geometric reconstruction. It appears that the current trend amongst practitioners of stereoscopic PIV is to use digital cameras to record the two views in the angular displacement configuration while incorporating the Scheimpflug condition. The use of calibration methods has also gained prominence over geometric reconstruction. Received: 15 April 1999/Accepted: 1 February 2000     

Tomographic particle image velocimetry

This paper describes the principles of a novel 3D PIV system based on the illumination, recording and reconstruction of tracer particles within a 3D measurement volume. The technique makes use of several simultaneous views of the illuminated particles and their 3D reconstruction as a light intensity distribution by means of optical tomography. The technique is therefore referred to as tomographic particle image velocimetry (tomographic-PIV). The reconstruction is performed with the MART algorithm, yielding a 3D array of light intensity discretized over voxels. The reconstructed tomogram pair is then analyzed by means of 3D cross-correlation with an iterative multigrid volume deformation technique, returning the three-component velocity vector distribution over the measurement volume. The principles and details of the tomographic algorithm are discussed and a parametric study is carried out by means of a computer-simulated tomographic-PIV procedure. The study focuses on the accuracy of the light intensity field reconstruction process. The simulation also identifies the most important parameters governing the experimental method and the tomographic algorithm parameters, showing their effect on the reconstruction accuracy. A computer simulated experiment of a 3D particle motion field describing a vortex ring demonstrates the capability and potential of the proposed system with four cameras. The capability of the technique in real experimental conditions is assessed with the measurement of the turbulent flow in the near wake of a circular cylinder at Reynolds 2,700.     

Digital particle image velocimetry

Digital particle image velocimetry (DPIV) is the digital counterpart of conventional laser speckle velocitmetry (LSV) and particle image velocimetry (PIV) techniques. In this novel, two-dimensional technique, digitally recorded video images are analyzed computationally, removing both the photographic and opto-mechanical processing steps inherent to PIV and LSV. The directional ambiguity generally associated with PIV and LSV is resolved by implementing local spatial cross-correlations between two sequential single-exposed particle images. The images are recorded at video rate (30 Hz or slower) which currently limits the application of the technique to low speed flows until digital, high resolution video systems with higher framing rates become more economically feasible. Sequential imaging makes it possible to study unsteady phenomena like the temporal evolution of a vortex ring described in this paper. The spatial velocity measurements are compared with data obtained by direct measurement of the separation of individual particle pairs. Recovered velocity data are used to compute the spatial and temporal vorticity distribution and the circulation of the vortex ring.     

Quantum nanospheres for sub-micron particle image velocimetry

Quantum Nanospheres™ (QNs) have been developed as a new type of flow-tracing particle for micron resolution particle image velocimetry (PIV). The 70 nm diameter QNs were created by conjugating quantum dots to polystyrene beads. The fluorescent QNs have a large Stokes’ shift and are impervious to photobleaching. The use of QNs as flow-tracing particles for micro-PIV was demonstrated by measuring fluid motion in a 30 × 300 μm channel. Using an interrogation region of 1 × 1,024 pixels and ensemble averaging 1,800 image pairs, the physical volume of the interrogation region was 117 μm × 117 μm × 2 μm.     

Real-time image processing for particle tracking velocimetry

We present a novel high-speed particle tracking velocimetry (PTV) experimental system. Its novelty is due to the FPGA-based, real-time image processing “on camera”. Instead of an image, the camera transfers to the computer using a network card, only the relevant information of the identified flow tracers. Therefore, the system is ideal for the remote particle tracking systems in research and industrial applications, while the camera can be controlled and data can be transferred over any high-bandwidth network. We present the hardware and the open source software aspects of the PTV experiments. The tracking results of the new experimental system has been compared to the flow visualization and particle image velocimetry measurements. The canonical flow in the central cross section of a a cubic cavity (1:1:1 aspect ratio) in our lid-driven cavity apparatus is used for validation purposes. The downstream secondary eddy (DSE) is the sensitive portion of this flow and its size was measured with increasing Reynolds number (via increasing belt velocity). The size of DSE estimated from the flow visualization, PIV and compressed PTV is shown to agree within the experimental uncertainty of the methods applied.     

Stereoscopic micro particle image velocimetry

A stereoscopic micro-PIV (stereo-μPIV) system for the simultaneous measurement of all three components of the velocity vector in a measurement plane (2D–3C) in a closed microchannel has been developed and first test measurements were performed on the 3D laminar flow in a T-shaped micromixer. Stereomicroscopy is used to capture PIV images of the flow in a microchannel from two different angles. Stereoscopic viewing is achieved by the use of a large diameter stereo objective lens with two off-axis beam paths. Additional floating lenses in the beam paths in the microscope body allow a magnification up to 23×. The stereo-PIV images are captured simultaneously by two CCD cameras. Due to the very small confinement, a standard calibration procedure for the stereoscopic imaging by means of a calibration target is not feasible, and therefore stereo-μPIV measurements in closed microchannels require a calibration based on the self-calibration of the tracer particle images. In order to include the effects of different refractive indices (of the fluid in the microchannel, the entrance window and the surrounding air) a three-media-model is included in the triangulation procedure of the self-calibration. Test measurement in both an aligned and a tilted channel serve as an accuracy assessment of the proposed method. This shows that the stereo-μPIV results have an RMS error of less than 10% of the expected value of the in-plane velocity component. First measurements in the mixing region of a T-shaped micromixer at Re = 120 show that 3D flow in a microchannel with dimensions of 800 × 200 μm² can be measured with a spatial resolution of 44 × 44 × 15 μm³. The stationary flow in the 200 μm deep channel was scanned in multiple planes at 22 μm separation, providing a full 3D measurement of the averaged velocity distribution in the mixing region of the T-mixer. A limitation is that this approach requires a stereo-objective that typically has a low NA (0.14–0.28) and large depth-of-focus as opposed to high NA lenses (up to 0.95 without immersion) for standard μPIV.     

New tracking algorithm for particle image velocimetry

The cross correlation tracking technique is widely used to analyze image data, in Particle Image Velocimetry (PIV). The technique assumes that the fluid motion, within small regions of the flow field, is parallel over short time intervals. However, actual flow fields may have some distorted motion, such as rotation, shear and expansion. Therefore, if the distortion of the flow field is not negligible, the fluid motion can not be tracked well using the cross correlation technique. In this study, a new algorithm for particle tracking, called the Spring Model technique, has been proposed. The algorithm can be applied to flow fields which exhibit characteristics such as rotation, shear and expansion.The algorithm is based on pattern matching of particle clusters between the first and second image. A particle cluster is composed of particles which are assumed to be connected by invisible elastic springs. Depending on the deformation of the cluster pattern (i.e., the particle positions), the invisible springs have some forces. The smallest force pattern in the second image is the most probable pattern match to the correspondent original pattern in the first image. Therefore, by finding the best matches, particle movements can be tracked between the two images. Three-dimensional flow fields can also be reconstructed with this technique.The effectiveness of the Spring Model technique was verified with synthetic data from both a two-dimensional flow and three-dimensional flow. It showed a high degree of accuracy, even for the three-dimensional calculation. The experimental data from a vortex flow field in a cylinder wake was also measured by the Spring model technique.     

A particle image velocimetry system for microfluidics

 A micron-resolution particle image velocimetry (micro-PIV) system has been developed to measure instantaneous and ensemble-averaged flow fields in micron-scale fluidic devices. The system utilizes an epifluorescent microscope, 100–300 nm diameter seed particles, and an intensified CCD camera to record high-resolution particle-image fields. Velocity vector fields can be measured with spatial resolutions down to 6.9×6.9×1.5 μm. The vector fields are analyzed using a double-frame cross-correlation algorithm. In this technique, the spatial resolution and the accuracy of the velocity measurements is limited by the diffraction limit of the recording optics, noise in the particle image field, and the interaction of the fluid with the finite-sized seed particles. The stochastic influence of Brownian motion plays a significant role in the accuracy of instantaneous velocity measurements. The micro-PIV technique is applied to measure velocities in a Hele–Shaw flow around a 30 μm (major diameter) elliptical cylinder, with a bulk velocity of approximately 50 μm s^-1. Received: 26 November 1997/Accepted: 26 February 1998     

Hybrid stereoscopic particle image velocimetry

 The technical aspects of a photographic stereo camera for three-dimensional particle image velocimetry are described herein. The hybrid concept of the camera combines advantages of the angular displacement and the translation method. The camera uses two CCD sensors in order to adjust the lens distances and angles to meet the Scheimpflug criterion and two coupled rotating mirrors for image shifting. An application to a jet flow with an exit velocity of 33 m/s demonstrates the succesfull optimization of the recording process. Received: 27 September 1996/Accepted: 6 March 1997     

Cinematographic system for high-image-density particle image velocimetry

A cinematographic system, which integrates the concepts of high-image-density PIV, laser scanning, and framing photography, allows temporal resolution of the order of one percent of the time scale of the largest vortical structures in the turbulent wake from a cylinder at a Reynolds number of 10,000. With this resolution in time, it is possible to track, in a continuous fashion, the patterns of streamwise vorticity in the near-wake. The authors are pleased to acknowledge the financial support of the National Science Foundation, the Office of Naval Research, and the Air Force Office of Scientific Research.     

Second-order accurate particle image velocimetry

 An adaptive, second-order accurate particle image velocimetry (PIV) technique is presented. The technique uses two singly exposed images that are interrogated using a modified cross-correlation algorithm. Consequently, any of the equipment commonly available for conventional PIV (such as dual head Nd: YAG lasers, interline transfer CCD cameras, etc.) can be used with this more accurate algorithm. At the heart of the algorithm is a central difference approximation to the flow velocity (accurate to order Δt ²) versus the forward difference approximation (accurate to order Δt) common in PIV. An adaptive interrogation region-shifting algorithm is used to implement the central difference approximation. Adaptive shifting algorithms have been gaining popularity in recent years because they allow the spatial resolution of the PIV technique to be maximized. Adaptive shifting algorithms also have the virtue of helping to eliminate velocity bias errors. The second- order accuracy resulting from the central difference approximation can be obtained with relatively little additional computational effort compared to that required for a standard first-order accurate forward difference approximation. The adaptive central difference interrogation (CDI) algorithm has two main advantages over adaptive forward difference interrogation (FDI) algorithms: it is more accurate, especially at large time delays between camera exposures; and it provides a temporally symmetric view of the flow. By comparing measurements of flow around a single red blood cell made using both algorithms, the CDI technique is shown to perform better than conventional FDI-PIV interrogation algorithms near flow boundaries. Cylindrical Taylor–Couette flow images, both experimental and simulated, are used to demonstrate that the CDI algorithm is significantly more accurate than conventional PIV algorithms, especially as the time delay between exposures is increased. The results of the interrogations are shown to agree quite well with analytical predictions and confirm that the CDI algorithm is indeed second-order accurate while the conventional FDI algorithm is only first-order accurate. Received: 15 June 2000/Accepted: 2 February 2001     

Twenty years of particle image velocimetry

The development of the method of particle image velocimetry (PIV) is traced by describing some of the milestones that have enabled new and/or better measurements to be made. The current status of PIV is summarized, and some goals for future advances are addressed.     

Flow analysis of two-dimensional pulsed jets by particle image velocimetry

A purely alternating jet without mean mass flux and a mixed pulsed jet containing an additional blowing component were investigated by particle image velocimetry (PIV). The jets issued from a two-dimensional slit connected to a converging nozzle, opening normally from a flat wall. The pulsation was driven by a loudspeaker. The mean velocity fields were characterized by the combination of downstream directional blowing and omni-directional suction. The velocity fluctuations were dominated by contra-rotating eddy pairs synchronized with the pulsation and formed at the jet edges during blowing. Phase-synchronized measurements permit the investigation of the averaged patterns and the cycle-to-cycle fluctuations of these vortices. The mean trajectories of vortex centers during a whole injection cycle show how large lateral jet expansions are achieved. For a purely alternating jet, the expansion takes place close to the slit. For a mixed pulsed jet, the vortices develop farther from the orifice. In addition, proper orthogonal mode decomposition demonstrates that only a few modes are required to represent the main events of the flow dynamics. Received: 10 August 1999 / Accepted: 10 January 2001     

Volume self-calibration for 3D particle image velocimetry

Planar self-calibration methods have become standard for stereo PIV to correct misalignments between laser light sheet and calibration plane. Computing cross-correlation between images from camera 1 and 2 taken at the same time, non-zero disparity vectors indicate rotational and translational misalignments relative to the coordinate system defined by a calibration plate. This approach works well for thin light sheets but fails for extended volumes recorded in 3D-PTV or tomographic PIV experiments. Here it is primarily necessary to correct calibration errors leading to triangulation errors in 3D-PTV or in degraded tomographic volume reconstruction. Tomographic PIV requires calibration accuracies of a fraction of a pixel throughout the complete volume, which is difficult to achieve experimentally. A new volumetric self-calibration technique has been developed based on the computation of the 3D position of matching particles by triangulation as in 3D-PTV. The residual triangulation error (‘disparity’) is then used to correct the mapping functions for all cameras. A statistical clustering method suitable for dense particle images has been implemented to find correct disparity map peaks from true particle matches. Disparity maps from multiple recordings are summed for better statistics. This self-calibration scheme has been validated using several tomographic PIV experiments improving the vector quality significantly. The relevance for other 3D velocimetry methods is discussed.     

Variational optical flow estimation for particle image velocimetry

We introduce a novel class of algorithms for evaluating PIV image pairs. The mathematical basis is a continuous variational formulation for globally estimating the optical flow vector fields over the whole image. This class of approaches has been known in the field of image processing and computer vision for more than two decades but apparently has not been applied to PIV image pairs so far. We pay particular attention to a multi-scale representation of the image data so as to cope with the quite specific signal structure of particle image pairs. The experimental evaluation shows that a prototypical variational approach competes in noisy real-world scenarios with three alternative approaches especially designed for PIV-sequence evaluation. We outline the potential of the variational method for further developments.The publications of the CVGPR Group are listed under .

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Treatment of interfaces in particle image velocimetry

A first-order accurate method of extending the capability of image velocimetry to interfaces is presented. In this method, the image fields are locally extended across interfaces using fields from the other image of an image pair. During this image parity exchange, the extension of the image fields amounts to locally reversing and reflecting the relative velocity field across the interface. Numerous experimental examples are given to demonstrate and validate the accuracy of the method. These are the plane Couette flow and the laminar pipe flow demonstrating straight rigid boundaries; uniform flow past a sphere and a sphere moving in a stagnant fluid demonstrating curved rigid surfaces; and a free-surface flow and a liquid–liquid interface flow demonstrating compliant interfaces. Received: 3 November 1998/Accepted: 18 August 1999     

Coherent structure identification from wavelet analysis of particle image velocimetry data

 A new technique based on wavelet transform is applied to bidimensional velocity fields obtained by particle image velocimetry (PIV) measurements, in order to extract and characterize swirling motion associated with coherent structures. The proposed technique is based on the selectivity property of the wavelet transform and permits the detection of regions of the flow field associated with coherent structures and their spatial localization. Furthermore, being the method based on the analysis of the local energy content at separated scales, it is possible to extract the typical wavenumber associated with structures and therefore the typical length-scale. The procedure is validated by the application to velocity vector fields obtained from PIV measurements in different flow conditions and turbulence levels. Results are compared with those obtained by other more standard procedures, and the advantages and limitations of the proposed method are then discussed. Received: 16 October 2000 / Accepted: 18 June 2001 Published online: 29 November 2001     

Measurement of spectrum with particle image velocimetry

The purpose of this paper is to show that the measurement of turbulent spectrum using wholefield velocity techniques such as particle image velocimetry (PIV) is possible. Toward this end, data from the axial plane of a self-similar turbulent axisymmetric jet, at a Reynolds number, based on Taylor microscale of 30 has been analyzed. The two-dimensional velocity data are first high-pass filtered, which educes the vortices. An automated method is then used to identify the vortices and measure their properties. By directly measuring the energy of the vortices, it is possible to plot the turbulence spectrum. The spectrum presented here shows the presence of energy containing and inertial regimes. However, the smallest scales have not been resolved in the measurements. The slope of the spectrum in the inertial subrange is about −1.6. The number of vortices in the two regimes have also been measured. The number of vortices in the energy containing regime is substantially smaller than those in the inertial subrange. The technique has been verified by analyzing another dataset. These results show that the direct measurement of vortex properties with reasonable confidence is possible using PIV and an appropriate vortex eduction technique.